FrF2Large | R Documentation |
Large regular fractional factorial 2-level designs in 8192 or more runs are provided: Resolution V designs in 8096 to 32768 runs with up to 120 factors according to the suggestion by Sanchez and Sanchez 2005 are automatically created (these are not necessarily optimal). Furthermore, manual generation of large regular fractional factorial designs via specification of generators is possible.
FrF2Large(nruns, nfactors = NULL, factor.names = if (!is.null(nfactors)){
if (nfactors <= 50)
Letters[1:nfactors]
else paste("F", 1:nfactors, sep = "")
} else NULL,
default.levels = c(-1, 1), ncenter = 0, center.distribute = NULL,
generators = NULL,
replications = 1, repeat.only = FALSE,
randomize = TRUE, seed = NULL, alias.info = 2, ...)
nrunsV(nfactors)
nruns |
Number of runs, must be a power of 2 (8192 to 32768). The number of runs must match the number of factors. Function |
nfactors |
is the number of 2-level factors to be investigated.
It can be omitted, if it is obvious from options |
factor.names |
a character vector of |
default.levels |
default levels (vector of length 2) for all factors for which no specific levels are given |
ncenter |
number of center points per block; |
center.distribute |
the number of positions over which the center points
are to be distributed for each block; if NULL (default), center points are
distributed over end, beginning, and middle (in that order, if there are fewer than three center points)
for randomized designs, and appended to the end for non-randomized designs.
for more detail, see function |
generators |
There are
a list of vectors with position numbers of base factors (e.g. c(1,3,4) stands for the interaction between first, third and fourth base factor) a vector of character representations of these interactions, e.g. “ACD” stands for the same interaction as above a vector of columns numbers in Yates order (e.g. 13 stands for ACD).
Note that the columns 1, 2, 4, 8, etc., i.e. all powers of 2, are reserved
for the base factors and cannot be used for assigning additional factors,
because the design would become a resolution II design. For looking up
which column number stands for which interaction, type e.g.
WARNING: Contrary to function |
replications |
positive integer number. Default 1 (i.e. each row just once).
If larger, each design run is executed replication times.
If Otherwise (default), the full experiment is first carried out once, then for the second replication and so forth. In case of randomization, each such blocks is randomized separately. In this case, replication variance is more likely suitable for usage as error variance (unless e.g. the same parts are used for replication runs although build variation is important). |
repeat.only |
logical, relevant only if replications > 1. If TRUE,
replications of each run are grouped together
(repeated measurement rather than true replication). The default is
|
randomize |
logical. If TRUE, the design is randomized. This is the default.
In case of replications, the nature of randomization depends on the setting of
option |
seed |
optional seed for the randomization process |
alias.info |
can be 2 or 3, gives the order of interaction effects for which
alias information is to be included in the |
... |
currently not used |
If generators are not explicitly specified, function FrF2Large
creates a
resolution V design according to the
rules by Sanchez and Sanchez (2005) for the specified number of factors in
the specified number of runs. The Sanchez and Sanchez article offers designs with
at least 1024 runs for 25 to 29 factors (1024 up to 33 factors with FrF2
),
at least 2048 runs for 30 to 38 factors (2048 up to 47 factors with FrF2
),
at least 4096 runs for 39 to 52 factors (4096 up to 65 factors with FrF2
),
at least 8192 runs for 53 to 69 factors (up to 65 factors in half the run size with FrF2
),
at least 16384 runs for 70 to 92 factors, (
at least 32768 runs for 93 to 120 factors.
For designs with up to 4096 runs, function FrF2
creates better automatic designs.
Therefore, function FrF2Large
is restricted to usage for larger designs.
Users can explicitly specify a design through specifying
generators via the generators
option. For up to 4096 runs, this is also possible
with function FrF2
, even with more flexibility. Therefore, manual design generation
with function FrF2Large
is also restricted to designs of at least 8192 runs.
Manual generation of large designs with the option generators
is limited by
computer memory only. nruns
must be at least large enough to accomodate the
rightmost generator column; for example, if generators contains an element ABEP
,
P
is the 15th base factor (15th letter in Letters
),
i.e. nruns
must be at least 2^15
=32768;
if the largest generator column number in Yates column notation is 4201,
nruns
must be at least 2^ceiling(log2(4201))
=8192.
Function nrunsV
invisibly returns the number of runs requested and
prints a message with the number of runs and the appropriate function.
Function FrF2Large
returns a data frame of S3 class
design
and has attached attributes that can be accessed
by functions desnum
,
run.order
and
design.info
.
The data frame itself contains the design with levels coded as requested.
If no center points have been requested, the design columns are factors with
contrasts -1
and +1
(cf. also contr.FrF2
); in case
of center points, the design columns are numeric.
The following attributes are attached to it:
desnum |
Design matrix in -1/1 coding |
run.order |
three column data frame, first column contains the run number in standard order, second column the run number as randomized, third column the run number with replication number as postfix; useful for switching back and forth between actual and standard run number |
design.info |
list with the entries
|
Since R version 3.6.0, the behavior of function sample
has changed
(correction of a biased previous behavior that might be relevant for the randomization
of very large designs).
For reproducing a randomized design that was produced with an earlier R version,
please follow the steps described with the argument seed
.
Ulrike Groemping
Mee, R. (2009). A Comprehensive Guide to Factorial Two-Level Experimentation. New York: Springer.
Sanchez, S.M. and Sanchez, P.J. (2005). Very Large Fractional Factorial and Central Composite Designs. ACM Transactions on Modeling and Computer Simulation 15, 362-377.
See also FrF2
for smaller regular fractional factorials and
oacat
for two non-regular resolution V fractional factorials (reported e.g. by
Mee 2009) for up to 19 factors in 256 runs or up to 63 factors in 2048 runs
## numbers of runs needed for resolution V designs in different numbers of factors
nrunsV(8)
nrunsV(18)
needed <- nrunsV(27)
needed
nrunsV(65)
nrunsV(71)
## Not run:
plan <- FrF2Large(nrunsV(75),75)
summary(plan)
## End(Not run)
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